Division

Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.

To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:

• p_i is divisible by x_i;
• x_i is not divisible by q_i.

Oleg is really good at division and managed to find all the answers quickly, how about you?

Input

The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.

Output

Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.

One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.

Example

Input

3 10 4 12 6 179 822

Output

10 4 179

Note

For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.

For the second pair, where p_2 = 12 and q_2 = 6, note that

• 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
• 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.

The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.

inputFormat

Input

The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.

outputFormat

Output

Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.

One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.

Example

Input

3 10 4 12 6 179 822

Output

10 4 179

Note

For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.

For the second pair, where p_2 = 12 and q_2 = 6, note that

• 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
• 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.

The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.

样例

3
10 4
12 6
179 822

10
4
179

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